I know when you go to register under historic registration they want a picture. Not sure how obvious the car is that there's a straight axle under it. If its sky high then they would probably notice. Insurance shouldn't be an issue as long as ya got modified type of insurance.
If I were doing it. I'd take pics of a stock car like your gasser and use those pics to register it then call and get modified insurance.
In nj there is no inspection at all for historic registered cars.